Skip to main content\(\newcommand{\sech}{\textrm{sech}}
\newcommand{\csch}{\text{csch}}
\newcommand{\reals}{\mathbb{R}}
\let\ds\displaystyle
\newcommand{\integral}[3][]{\int#1 #2 \;d#3}
\newcommand{\dsintegral}[3][]{\ds\int#1 #2 \;d#3}
\newcommand{\veci}{\hat{\imath}}
\newcommand{\vecj}{\hat{\jmath}}
\newcommand{\veck}{\hat{k}}
\newcommand{\vecr}{\vec{r}}
\newcommand{\vecu}{\vec{u}}
\newcommand{\vecv}{\vec{v}}
\newcommand{\vecw}{\vec{w}}
\newcommand{\vecn}{\vec{n}}
\newcommand{\T}{\widehat{T}}
\newcommand{\N}{\widehat{N}}
\newcommand{\B}{\widehat{B}}
\newcommand{\Grad}{\text{Grad}}
\newcommand{\Div}{\text{Div}}
\newcommand{\Curl}{\text{Curl}}
\newcommand{\Rot}{\text{Rot}}
\newcommand{\del}{\overrightarrow{\nabla}}
\newcommand{\C}{\mathcal{C}}
\newcommand{\veclong}{\overrightarrow}
\renewcommand{\vector}[1]{\left\langle #1 \right\rangle}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
